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Unformatted text preview: sets are VI, . .. , vm and vm+b . .. , Vm+ n ' the 1 1 0 0 adjacency matrix is 1 1 0 0 3. (a) [BB] The (3,5) entry of A3 is the number of walks of length 3 from C to E and, hence, equals 5. The (2,2) entry of A3 is the number of walks oflength 3 from B to itself, hence, equals 2. (b) The (3,5) entry of A3 equals 2. The (2,2) entry of A3 equals 4. 4. [BB] Each 1 represents an edge. Each edge ViVj contributes two l's to the matrix, in positions (i,j) and (j, i). The number of l's is twice the number of edges. 5. The ith entry on the diagonal of A3 is the number of walks of length 3 from Vi to itself. However, a closed walk of length 3 in a graph must give a triangle. Every triangle can be walked in exactly two different directions. Hence, the number of walks of length 3 is twice the number of triangles....
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
- Summer '10
- Graph Theory